GPS/Dead Reckoning Navigation with Kalman Filter Integration

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  • GPS/Dead Reckoning Navigation with Kalman Filter IntegrationPaul Bakker

  • Kalman FilterThe Kalman Filter is an estimator for what is called the linear-quadratic problem, which is the problem of estimating the instantaneous state of a linear dynamic system perturbed by white noise by using measurements linearly related to the state but corrupted by white noise. The resulting estimator is statistically optimal with respect to any quadratic function of estimation error [1]

  • Kalman Filter UsesEstimationEstimating the State of Dynamic SystemsAlmost all systems have some dynamic componentPerformance AnalysisDetermine how to best use a given set of sensors for modeling a system

  • Basic Discrete Kalman Filter Equations

  • Automobile Voltimeter Example

  • Time 50 Seconds

  • Time 100 Seconds

  • Global Positioning System

  • GPS24 or more satellites (28 operational in 2000)6 circular orbits containing 4 or more satellitesRadii of 26,560 and orbital period of 11.976 hoursFour or more satellites required to calculate users position

  • GPS Satellite Signals

  • GPS code sync Animation the Pseudo Random codes match up the receiver is in sync and can determine its distance from the satellite

  • Receiver Block Diagram

  • Navigation Pictorial

  • Position Estimates with Noise and Bias Influences

  • Differential GPS ConceptReduce error by using a known ground reference and determining the error of the GPS signalsThen send this error information to receivers

  • GPS Error Sources

  • GDOP

  • Example of Importance of Satellite ChoiceThe satellites are assumed to be at a 55 degree inclination angle and in a circular orbitSatellites have orbital periods of 43,082

    Right AscensionAngular Location

  • GDOP (1,2,3,4) vs. (1,2,3,5)Optimum GDOP for the satellitesThe smaller the GDOP the better

    GDOP Chimney (Bad) 2 of the 4 satellites are too close to one another dont provide linearly independent equations

  • RMS X ErrorGraphed above is the covariance analysis for RMS east position errorUses Riccati equations of a Kalman FilterOptimal and Non-Optimal are similar

  • RMS Y ErrorCovariance analysis for RMS north position error

  • RMS Z ErrorCovariance analysis for vertical position error

  • Clock Bias ErrorCovariance analysis for Clock bias error

  • Clock Drift ErrorCovariance analysis for Clock drift error

  • Questions & References[1] M. S. Grewal, A. P. Andrews, Kalman Filtering, Theory and Practice Using MATLAB, New York: Wiley, 2001